olymmath

HMMT November 2010 E6

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What is the sum of the positive solutions to 2x2−x⌊x⌋=52 x^{2}-x\lfloor x\rfloor=5, where ⌊x⌋\lfloor x\rfloor is the largest integer less than or equal to xx ?

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{3+\sqrt{41}+2 \sqrt{11}}{4}

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